Tony Abbott’s first international test as prime minister is also likely to be his toughest, when he meets with Indonesian President Susilo Bambang Yudhoyono today. It will be a remarkable feat if he can pull the policy fat from the diplomatic fire.

In the balance lies Australia’s critical relationship with Indonesia. Not only has Abbott’s signature “turn back the boats” policy been comprehensively rejected by the Indonesian government, Indonesia has now fired a real warning shot across Australia’s diplomatic bow.

The “unintentional” release of the notes of the conversation between foreign ministerial counterparts Julie Bishop and Marty Natalegawa late last week was a blunt warning: the issue may blow up further if not resolved quickly.

Abbott’s dismissal of his asylum-seeker boats policy as a “passing irritant” in the wider bilateral relationship with Indonesia will be viewed as arrogant. Arrogance is a quality not much appreciated in Indonesian political society, and especially not from Australian politicians. It is also incorrect to treat it so lightly, given the issue is now central to a complex web of arrangements.

At primary risk is Indonesia’s existing co-operation with Australia against the people-smuggling trade. This then segues into other areas of security co-operation, including on terrorism and wider security issues.

The awkwardness of Abbott’s visit has been underscored by the inept intervention by former foreign minister Alexander Downer on Thursday. Downer’s status as a former Coalition foreign minister means his “pious rhetoric” comment against Indonesia will be read in Jakarta as informing the Australian perspective.

Asylum-seeker boats leaving Indonesia are a private and, at most, criminal matter. If they do breach Australian sovereignty, it is not a consequence of Indonesian state policy.

By contrast, Australia’s “Operation Sovereign Borders” of sending boats in international waters back to Indonesia is official state policy. On this, Downer blundered and Indonesia holds the high diplomatic ground.

Abbott distancing himself from Downer’s statement will be seen as just as unconvincing as Natalegawa’s claim of the “unintentional release” of notes of his conversation with Bishop. The distinction on issues of sovereignty and official policy can be expected to be brought to Abbott’s attention .

Australia has recently enjoyed a positive relationship with Indonesia, overwhelmingly because of the benign political character of President Yudhoyono. But Natalegawa’s release of the Bishop conversation notes reflects a growing impatience with Australia. If Abbott persists, bilateral relations could quickly collapse to the lows of 1999, when Australia intervened in East Timor.

Indonesia has always been important to Australia, but is increasingly so. Its economy, growing at over 6% a year, is due to overtake Australia’s by 2017, while it is Australia’s 13th biggest trading partner (and growing).

Importantly, Indonesia is Australia’s pivot into ASEAN, including the security-focused ASEAN Regional Forum, as well as a key partner in APEC and wider regional relations. Add to that key sea lanes and air routes, and you have a relationship that Australia cannot afford to get wrong. All of this will be on the table when Abbott and Yudhoyono meet.

The question will be, then, whether Abbott throws overboard his “turning back the boats” policy in favour of greater regional co-operation. The alternative might instead be looking at throwing overboard a large part of the bilateral relationship with our closest neighbour.